Joint Antenna and Propagation Model Parameter Estimation using RSS measurements

Parinaz Kasebzadeh, Carsten Fritsche, Emre Özkan, Fredrik Gunnarsson and Fredrik Gustafsson

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Original Publication: Parinaz Kasebzadeh, Carsten Fritsche, Emre Özkan, Fredrik Gunnarsson and Fredrik Gustafsson, Joint Antenna and Propagation Model Parameter Estimation using RSS measurements, 2015, 18th International Conference on Information Fusion, Washington D.C, USA, July 6-9, 2015.

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Joint Antenna and Propagation Model Parameter Estimation using RSS measurements

Parinaz Kasebzadeh, Carsten Fritsche, Emre Ozkan,¨ Fredrik Gunnarsson†, Fredrik Gustafsson Department of Electrical Engineering, Linkoping¨ University, Linkoping,¨ Sweden Email: [email protected], {carsten, emre, fredrik}@isy.liu.se † Ericsson Research, Linkoping,¨ Sweden, Email: [email protected]

Abstract—In this paper, a semi-parametric model for RSS management perspective, the positioned radio measurement measurements is introduced that can be used to predict coverage enables an operator to identify where issues such as poor in cellular radio networks. The model is composed of an empirical coverage or excessive interference are located. Commonly, log-distance model and a deterministic antenna gain model that accounts for possible non-uniform base station antenna radiation. one distinguish between network-centric and mobile-centric A least-squares estimator is proposed to jointly estimate the path solutions. In the former, a network entity estimates the position loss and antenna gain model parameters. Simulation as well as of a terminal, possibly based on measurements reported by experimental results verify the efficacy of this approach. The the terminal. Moreover, in the latter, the terminal is provided method can provide improved accuracy compared to conventional with assistance data to enable it to estimate its position. path loss based estimation methods. The position estimate may also be based on a measurement snapshot, or a time series of measurements. The measurements I.INTRODUCTION are typically related to time of arrival (TOA), received signal The high pace of development of geographical positioning strength (RSS) and angle of arrival (AoA) of transmitted methods along with tracking mobile users might be routed reference signals, or combinations thereof [12]. to various sources. Navigation, people and assets tracking, RSS measurements are typically reported from the terminal location based security and coordination of emergency and to the base station for other reasons than positioning, such as maintenance responses to accidents, interruptions of essential handover from a serving cell to a target cell, radio resource services, mapping the location of disaster victims, cellular management in general, or to assess the properties of the system design and management are examples of different radio conditions in a cell as part of network management. applications and services which rely on the accurate position Therefore, they can be seen as readily available. In a po- estimation [1]. sitioning context, RSS measurements are used for ranging The first enabling Global Navigation Satellite System and fingerprinting [12]. Recently, it has also been shown (GNSS)-based positioning methods such as those based on how RSS measurements together with information about base Global Positioning System (GPS) are still in use in many station antenna properties, can be used to estimate the angle applications. Briefly speaking, those methods are based on of arrival [13]. Also, knowledge about the serving sector cell signals transmitted from satellites and as mentioned are a together with information about the sectorized antenna, yields primary source of location estimations for many applications. a crude estimate of the angle of arrival for the terminal. The However, the negative-affecting factors impose the necessity performance of positioning based on such bearing estimates of evolution of conventional approaches. For example, outdoor is assessed in [14], and in [12]. The latter also address the environments such as ”urban canions”, bad weather conditions positioning performance given RSS measurements used for resulting in poor signals, and indoor environments where the ranging, given a parametric radio propagation model. signal is totally non-accessible, other alternatives must be Two main approaches that are widely studied in the liter- applied. Assisting GNSS signals with other wireless networks ature that use RSS measurements for positioning purposes, such as the Third Generation Partnership Project (3GPP), are channel modeling [15], [16] and fingerprinting [17], [18]. Long Term Evolution (LTE) or IEEE 802.11, that is studied Both of these two however, suffer from lack of considering widely in the literature (for different applications, see [2]– simultaneous effects of channel and antenna parameters on [4]), is one solution to increase both availability of service RSS measurements they use for positioning algorithms. More- and the accuracy of estimation. On the other hand, in indoor over, the change of channel and antenna parameters based environments, relying on available Wireless LAN (WLAN) on the instantaneous propagation condition is also neglected. infrastructures for position estimation purposes is investigated If detailed propagation model calibration is ruled out, the for a long term where, [5]–[11] can be seen as examples. applicability of the RSS measurements for ranging is subject Cellular radio network positioning can be seen as an alter- to significant uncertainty. Such uncertainty can be considered native to Assisted GPS (A-GPS) systems mentioned above, in the positioning algorithm, but still with fairly inaccurate when the latter is unavailable. Example use cases include positioning performance as a result [19]. emergency call positioning. Furthermore, from a radio network An alternative is to take advantage of the recent devel- opment of smartphones, capable of logging accurate GPS the MS position (antenna gain model). We further make positions and RSS measurements. Thereby, it is possible the common assumption that the RSS measurement is time- to retrieve such trajectories at a calibration entity and use averaged, such that temporal effects resulting from small-scale for model parameter calibrations. Traditionally, close range fading can be neglected. Hence, the proposed semi-empirical measurements have been used to measure the antenna gain in model for the RSS measurement in logarithmic scale (dBm) detail, while avoiding significant propagation effects. More- can be written as over, positioned RSS measurements have been modified in y = P − {L(x) − G (x)} + e, (2) consideration of the antenna model to determine corresponding T ant T RSS measurements from an isotropic antenna, which in turn where x , [d, φ, ψ] is the vector holding the relative position has been used to estimate the parameters of the propagation information of the MS with respect to the BS antenna, PT is model. the BS transmit power in dBm, and e is a statistical term which In this paper, we present a method to jointly estimate both accounts for the errors resulting from quantization, slow fading the antenna and propagation model parameters using posi- and other effects that are not captured by the propagation tioned RSS measurements. The rest of the paper is organized model. The error term e is modeled with a zero-mean Gaussian as follows: In Section II a semi-empirical model for RSS distribution with variance σ2. measurement is presented. Section III addresses requirements for joint propagation model and antenna parameter estima- A. Path Loss Model tion representation. Section IV evaluates performance of the A path loss (PL) model presents signal attenuation in space. proposed model using simulations followed by verifications In this work, the log-distance model is used as it forms the applied on real-field data provided in Section V. Finally, basis of most models available in the literature [22], [5]. The Section VI concludes the work. log-distance model is given by  d  II.RSS MEASUREMENTMODEL L(d) = A + 10B log , (3) 10 d The RSS measurement y can be expressed by the following 0 general model where A is the reference path loss, B is the path loss exponent, d is the Euclidean distance between the MS and BS, and d0 y = h(x) + e, (1) represents the distance at which the reference path loss A is where h(x) is a propagation model (sometimes also called determined. The value of d0 generally depends on the cell size, radio channel) that accounts for propagation effects, such as and values that can be typically found are 100 m or 1 km. attenuation, diffraction, or reflection, that the electromagnetic B. Antenna Gain Model wave is affected by, when traveling between the Mobile Station Base station antenna modeling mainly concerns crude mod- (MS) and the Base Station (BS). Here, x denotes a (vector) els that capture the far-field (at some distance from the variable providing relative position dependent information of antenna) gain in various directions. Models, that have become the MS and the BS and/or the environment, and e represents popular in recent years are separated into one horizontal plane a statistical noise term (here assumed to be additive) that model G (φ) and one vertical plane model G (ψ), and the accounts for effects that cannot be captured by the propagation h v combined antenna gain is merely the two model contributions model. added together in logarithmic scale according to The propagation models can be broadly categorized into three types: deterministic, empirical, and semi-empirical mod- Gant(φ, ψ) = Gh(φ) + Gv(ψ). (4) els [1]. The deterministic models are based on techniques such as ray tracing or ray launching that require accurate knowledge Simplified models neglect the vertical component and model of the environment such as high resolution building data. only the horizontal antenna gain. In this work, we consider These models are very accurate, but also the most complex the antenna gain model proposed in [23] that is also adopted ones. Empirical models use heuristic equations that have been for the radio network evaluations in 3GPP. The horizontal gain derived from extensive measurement campaigns. These models model is given by ! are very simple, but less accurate than their deterministic φ − φ 2 G (φ) = G − min 12 0 ,G , (5) counterparts. Among the most popular empirical models are h max φ h,min the Okumura-Hata and COST 231 models [1], [20], [21]. h Semi-empirical models are composed of both deterministic where Gmax denotes the maximum antenna gain in dBi, and empirical models and provide a good compromise between −180◦ < φ ≤ 180◦ is the antenna azimuth angle defined in accuracy and complexity. the xy-plane, counted counter-clockwise from the positive x- In the following, we introduce a semi-empirical propagation axis, φh is the antenna’s horizontal bandwidth in degree, which model for the RSS measurement. It combines an empirical represents the bandwidth at which the antenna gain is half of distance-dependent propagation loss (or path loss) model L(x) the maximum gain (also known as half-power beamwidth), φ0 with a deterministic model Gant(x) representing the possible is the antenna angle in degree pointing into the direction of non-uniform radiation of the BS antenna with respect to maximum gain (antenna boresight angle), and Gh,min denotes the front-to-back ratio measured in dB, given the relative dif- With this simplification, the maximum likelihood estimate of ference between antenna beam direction gain Gh (φ0) = Gmax the parameters becomes tractable, and can be found according ◦ and the back lobe gain Gh (φ0 + 180 ) = Gmax − Gh,min. The to vertical antenna gain is modeled with θˆML = arg max p(Y |θ), (8)  2 ! θ∈Θ ψ − ψetilt Gv(ψ) = max −12 ,Gv,min , (6) where Y is an independent and identically distributed (i.i.d.) ψv sequence of m RSS measurements and θ are the unknowns. where −90◦ < ψ ≤ 90◦ is the negative antenna elevation Under the Gaussian noise assumption the maximum likelihood angle relative to the horizontal plane, i.e. ψ = 90◦ is down- solution is equivalent to the least squares estimator. The wards, ψ = 0◦ is along the horizontal plane, and ψ = −90◦ RSS measurement becomes linear in the following unknown −2 −2 T is upwards. The angle ψetilt given in degree is the electrical parameters θ = [A, B, φh , ψv ] , where it has been assumed antenna downtilt that models the angle downwards from the that the antenna main direction φ0, the electrical downtilt ψetilt, horizontal plane at which the antenna is electrically directed, the transmission power PT and the maximum antenna gain Gm ψv is the antenna’s half-power beamwidth in the vertical all are known. The least squares estimate is given as direction, and G is the side lobe level in dB of the vertical v,min θˆLS = θˆML = (HT H)−1HT Z, pattern that represents the side lobe gain level in relation to the (9) antenna vertical beam direction gain. As an example, Figure 1 where illustrates the horizontal antenna gain model (5), together with  d1 2 2  1 10 log10( ) 12(φ1 − φ0) 12(ψ1 − ψetilt) real data from an antenna, see [23] for an additional example d0 . . . .  including the vertical antenna gain model. H , . . . .  , dm 2 2 1 10 log ( ) 12(φm − φ0) 12(ψm − ψ ) 10 d0 etilt (10) 20 and   PT + Gmax − y1 10  .  Z ,  .  . (11) PT + Gmax − ym 0 An unbiased estimate of the noise variance σˆ2 is given by -10 m 1 X σˆ2 = (ˆz − z )2, (12) m − 1 i i -20 i=1

where zˆi’s are found by plugging in the least squares solution Horizontal Antenna Gain [dB] LS -30 into Zˆ = Hθˆ . As already stated earlier, the BS transmit Real Data Parametrized Model power PT and maximum antenna gain Gmax can not be esti- -40 mated separately from the path loss parameter A. Therefore, it -150 -100 -50 0 50 100 150 is reasonable to assume them a priori known, or to approximate Horizontal Angle Rel. Main Direction [deg] them using nominal values taken from antenna specification Fig. 1: Illustration of horizontal antenna gain pattern documents, or by lumping these parameters together forming ˜ the new (unknown) parameter A = PT − A + Gmax, that is to III.JOINT PATH LOSSAND ANTENNA PARAMETER be estimated instead. ESTIMATION For the main lobe assumption to hold, the horizontal and vertical angles needs to be close to the antenna main beam The joint contribution of the attenuation due to path loss and direction. This implies the following boundary conditions to the antenna gain enter the measurement equation additively. be satisfied: Hence identification of some parameters is not possible due r to unobservability. For instance, it is not possible to estimate Gh,min |φ − φ0| < φh , (13a) the reference path loss A and the maximum antenna gain Gmax 12 r separately. Another issue with the joint parameters estimation −G |ψ − ψ | < ψ v,min . (13b) is that the antenna gain is modeled different inside and outside etilt v 12 the main lobe using min(, ) and max(, ) functions which Clearly, the boundary conditions depend on the unknown results in non-linear equations. Under the assumption that the parameters φ and φ , making it difficult to motivate consid- main lobe components are dominant, the contribution of the h v ering only those RSS measurements in the estimation process antenna gain simplifies to that fulfill the above requirements. However, it is always  2  2 possible to use smaller values for the parameters in (13) ˜ φ − φ0 ψ − ψetilt Gant(φ, ψ) = Gmax −12 −12 . (7) deviating from the nominal values that can be typically found φh ψv in antenna specification documents, implying a smaller main that have been introduced above. The estimation results are lobe area from which RSS measurements can be used in shown in Table II and III, respectively. the estimation process. However, these parameters should be carefully selected in order to avoid deteriorating the estimation TABLE II: Estimation results for true boundary conditions results, for instance by assuming a too small main lobe area. ◦ ◦ Parameter A [dB] B [dB] φh [ ] ψv [ ] σ [dB] IV. SIMULATED DATA EXPERIMENTS True 100 2.3 65 7 4 In this section, the performance of the algorithm proposed Est. (m = 1e3) 99.46 2.23 64.88 6.83 4.07 Est. (m = 2e3) 99.86 2.27 64.92 6.93 3.96 in the previous section is tested on simulated data. The RSS Est. (m = 5e4) 100.37 2.33 64.99 7.11 4.03 measurements are generated from (2) using the parametrized antenna gain model, see (5) and (6). In Table I, the path loss It can be observed that the estimation results improve and antenna gain model parameters are listed that have been as the number of RSS measurements m used in the least- used in the simulations. The antenna parameters correspond squares solution is increased. It can be also seen that there is to typical values that can be found in antenna specifications. essentially no difference whether the true boundary conditions B 2 The path loss exponent is typically between (free-space or the approximate boundary conditions are used to select the 4 propagation) and (dense urban environment) and has been RSS measurements for the parameter estimation process. chosen slightly above the free-space propagation, in order to better reflect outdoor BS deployments in rural areas. For the antenna parameters given in Table I, it is possible to derive TABLE III: Estimation results for approximate boundary conditions the boundary conditions (13), where RSS measurements shall ◦ ◦ Parameter A [dB] B [dB] φh [ ] ψv [ ] σ [dB] be collected in order to not violate the simplified antenna gain True 100 2.3 65 7 4 model assumption (7). Est. (m = 1e3) 100.25 2.35 64.83 7.09 3.97 Est. (m = 2e3) 99.87 2.36 64.99 6.91 4.06 TABLE I: List of path loss and antenna model parameters Est. (m = 5e4) 100.05 2.32 64.98 7.02 4.01 Parameter Description Value PT BS transmit power 32 dBm As an example, the estimation results of the path loss A Reference path loss 100 dB parameters are shown in Figure 2 for the method using the B 2.3 Path loss exponent dB approximate boundary conditions. It can be observed that d0 Reference Distance 1000 m σ Error standard deviation 4 dB the estimated path loss slope is in good agreement with the Gmax Maximum gain 18 dBi true slope. Note, that the RSS measurements still contain the ◦ φh Horizontal beamwidth 65 contribution from the antenna gain and thus the true and φ Boresight angle 0◦ 0 estimated slope do not follow the trend of the RSS values. Gh,min Front-to-back ratio 30 dB ◦ ψetilt Vertical downtilt 9 For comparison purposes, we have also included the path ◦ ψv Vertical beamwidth 7 loss slope when the estimator is only estimating the path loss Gv,min Side lobe level −18 dB parameters, i.e. Gant = 0 in the estimator model. In this case, hBS BS height 30 m we have a model mismatch and the path loss slope follows It is easy to show that for an antenna with the parameters the trend of the RSS measurements, as expected. given in Table I, the requirements for the main lobe area are given by −103◦ ≤ φ ≤ 103◦ and 0.4◦ ≤ ψ ≤ 17.6◦, respec- m=1000 -20 tively. The azimuth requirement corresponds to more than the RSS measurements ◦ entire 120 sector the antenna normally covers (Note, that in -30 True model Estimated model cellular radio networks each cell site is normally equipped Model mismatch with three antennas each covering a 120◦ sector). With a -40 relative antenna height of 30 m, this means that the elevation -50 requirements are valid for distances from the BS between 30 m/ tan(17.6◦) ≈ 95 m and 30 m/ tan(0.4◦) ≈ 4030 m. -60

On the other hand, if we assume smaller values for the half- RSS [dB] ◦ ◦ -70 power beamwidth, e.g. φh = 60 and φv = 6 , the main lobe area from which RSS measurements could be used in -80 the estimation process, would shrink to −95◦ ≤ φ ≤ 95◦ and 1.7◦ ≤ ψ ≤ 16.4◦, yielding distances from the BS between -90 102 1040 m and m, which is still acceptable. -100 Based on the above results, i.i.d. RSS measurements are 102 103 generated by distributing MS positions uniformly within log-distance [m] the main lobe area. Here, we distinguish between the true Fig. 2: Path loss estimation results for simulated data using approx- boundary conditions and the approximate boundary conditions imate boundary conditions and m = 1000. −75 For the model mismatch case, we also included the estima- 400 tion results for different number of RSS measurements taken −80 200 from the approximate boundary conditions, which are shown −85

0 in Table IV. It is now also observed that the error standard −90 deviation is much larger, which is due to the compensation of −200 −95 unmodeled antenna gain variations. The benefits of adopting −100 −400 a joint antenna and propagation model in comparison to only y[m] −105 a propagation model is this evident. −600 −110

TABLE IV: Estimation results for model mismatch and approximate −800 −115 boundary conditions −120 −1000

Parameter A [dB] B [dB] σ [dB] −125 −1200

True 100 2.3 4 −200 0 200 400 600 800 1000 1200 1400 1600 Est. (m = 1e3) 103.37 3.98 8.40 x[m] Est. (m = 2e3) 103.21 3.84 8.55 Fig. 3: The RSS values collected along different trajectories around Est. (m = 5e4) 103.39 4.01 8.68 the antenna. Antenna location is shown by the big circle

V. REAL DATA EXPERIMENTS scattering. Furthermore, the residual standard deviation of 7 The proposed joint antenna and propagation model de- dB is in the expected range of 6-10 dB [12]. scribed in the previous section is also verified with real- field measurements. The measurements are collected in a TABLE V: Estimation results for real data experiments using only rural/suburban area, with an Android app for logging A-GPS horizontal antenna gain pattern ◦ and RSS [24]. The smartphone was configured to camp on a Parameter A [dB] B [dB] φh [ ] σ [dB] 3GPP LTE/E-UTRAN network, which means that the logging Est. (m = 1252) 152.6 2.9675 79.5823 7.0265 reflects Reference Signal Received Power (RSRP). In order to identify the parameters accurately, a direct LOS Figure 4 illustrates the fit of the propagation model com- between the MS and BS is preferable. One base station is ponent, which indicates a good fit. These brief evaluations chosen in an area where buildings and similar structures that indicate the relevance and benefits of joint antenna and prop- can obscure a direct LOS are rather sparse. The selected base agation model parameter estimation. station feeds antennas mounted on a mast which is 30 m high.

The BS serves three cells each covering 120 degrees, and one −70 ◦ RSS measurements of the cells (with an antenna boresight direction φ0 = −30 ) Estimated model is used for evaluation purposes. The antenna associated to −80 the cell has a halfpower beamwidth of 60 degrees. However, not that this is the beamwidth observed near the antenna. Signal scattering will spread the signals, effectively creating −90 an antenna that is perceived to be wider by a distant observer. It is therefore expected that the estimated horizontal halfpower −100 beamwidth is slightly wider than the nominal beamwidth of RSS [dB]

60 degrees, and the vertical halfpower beamwidth wider than −110 the nominal bandwidth of 7 degrees. The measurements are collected over several trajectories around the site as depicted in Figure 3. In the same figure, −120 the RSS values are also presented with colors. −130 2 3 Measurements were selected that are assumed to be in the 10 10 horizontal main lobe of the antenna, with boundary conditions log−distance [m] ◦ |φ − φ0| ≤ 50 . The region is quite flat and the trajectories Fig. 4: RSS measurements together with estimated path loss model are not in close vicinity of the antenna. Therefore there is not much variety in vertical angles. The contribution from the ver- tical antenna gain is expected to be smaller than 0.1dB under VI.CONCLUSION the assumption of nominal value of the parameters. Hence its In this paper we propose an algorithm for joint antenna effect is neglected for the scenario, and the vertical antenna and propagation model parameter estimation. The associated gain component is omitted from the joint model. The estimated parameter estimation problem can be formulated as a least parameters under these assumptions are given in Table V. As squares problem, which enables efficient estimation of the expected, the estimated effective horizontal antenna halfpower model parameters. The problem is considered tractable given beamwidth φh is wider than the nominal beamwidth due to measurement trajectories with positioned RSS measurements within the main lobe of the antenna. The proposed method [18] J. Yin, Q. Yang, and L. Ni, “Learning adaptive temporal radio maps has been evaluated using both simulated and real RSS mea- for signal-strength-based location estimation,” Mobile Computing, IEEE Transactions on, vol. 7, no. 7, pp. 869–883, July 2008. surement with promising results. The results also indicate that [19] P. Tarr´ıo, A. M. Bernardos, and J. R. 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